Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}. Find (i) A x (B ∩

1.	Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}. Find (i) A x (B ∩ C) (ii) (A x B) ∩ (A x C) (iii) A x (B∪C) (iv) (A x B)∪(A x C)
Answer» (i) B∩C={4} A x (B∩C) = (1,4), (2, 4), (3,4)} (ii) A x B = {(1, 3), (1,4), (2, 3), (2, 4), (3, 3), (3, 4)} A x C = {(1, 4), (1, 5) (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)} (A x B)∩(A x C)= {(1, 4), (2, 4), (3, 4)} (iii) B ∪ C={3,4, 5, 6} ∴ A x (B ∪ C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)} (iv) A x B = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)} A x C = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)} (A x B)∪(A x C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6) (3, 3), (3, 4), (3, 5), (3,6)}.

Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}. Find (i) A x (B ∩ C) (ii) (A x B) ∩ (A x C) (iii) A x (B∪C) (iv) (A x B)∪(A x C)

Answer»

(i) B∩C={4}

A x (B∩C) = (1,4), (2, 4), (3,4)}

(ii) A x B = {(1, 3), (1,4), (2, 3), (2, 4), (3, 3), (3, 4)}

A x C = {(1, 4), (1, 5) (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}

(A x B)∩(A x C)= {(1, 4), (2, 4), (3, 4)}

(iii) B ∪ C={3,4, 5, 6}

∴ A x (B ∪ C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)}

(iv) A x B = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}

A x C = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}

(A x B)∪(A x C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6) (3, 3), (3, 4), (3, 5), (3,6)}.